source: sasmodels/sasmodels/models/lamellarFFHG.py @ dc02af0

# Note: model title and parameter table are inserted automatically
r"""
This model provides the scattering intensity, *I(q)*, for a lyotropic lamellar phase where a random distribution in
solution are assumed. The SLD of the head region is taken to be different from the SLD of the tail region.

*2.1.31.1. Definition*

The scattering intensity *I(q)* is

.. math::

    I(Q) = 2\pi{P(Q) \over (2(|delta|\ H +|delta|\ T) Q^2)

The form factor is

.. image:: img/lamellarFFHG_.jpg

where |delta|\ T = tail length (or *tail_length*), |delta|\ H = head thickness (or *h_thickness*),
|drho|\ H = SLD(headgroup) - SLD(solvent), and |drho|\ T = SLD(tail) - SLD(solvent).

The 2D scattering intensity is calculated in the same way as 1D, where the *q* vector is defined as

.. math::

    Q = \sqrt{Q_x^2 + Q_y^2}

The returned value is in units of |cm^-1|, on absolute scale. In the parameters, *sld_tail* = SLD of the tail group,
and *sld_head* = SLD of the head group.

==============  ========  =============
Parameter name  Units     Default value
==============  ========  =============
background      |cm^-1|   0.0
head_sld        |Ang^-2|  3e-06
scale            None      1
solvent_sld     |Ang^-2|  6e-06
head_length     |Ang|     10
tail_length     |Ang|     15
sld (tail)      |Ang^-2|  0
==============  ========  =============

.. image:: img/lamellarFFHG_138.jpg

*Figure. 1D plot using the default values (w/1000 data point).*

Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research
(Kline, 2006).

REFERENCE

F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502

also in J. Phys. Chem. B, 105, (2001) 11081-11088

*2014/04/17 - Description reviewed by S King and P Butler.*
"""

from numpy import pi, inf

name = "lamellar_FFHG"
title = "Random lamellar phase with Head Groups "
description = """\
        [Random lamellar phase with Head Groups]
                I(q)= 2*pi*P(q)/(2(H+T)*q^(2)), where
                P(q)= see manual
                layer thickness =(H+T+T+H) = 2(Head+Tail)
                sld = Tail scattering length density
                sld_head = Head scattering length density
                sld_solvent = solvent scattering length density
                background = incoherent background
                scale = scale factor
"""

parameters = [
#   [ "name", "units", default, [lower, upper], "type",
#     "description" ],
    [ "tail_length", "Ang",  15, [0, inf], "volume",
      "Tail thickness" ],
    [ "head_length", "Ang",  10, [0, inf], "volume",
      "head thickness" ],
    [ "sld", "1e-6/Ang^2", 0.4, [-inf,inf], "",
      "Tail scattering length density" ],
    [ "head_sld", "1e-6/Ang^2", 3.0, [-inf,inf], "",
      "Head scattering length density" ],
    [ "solvent_sld", "1e-6/Ang^2", 6, [-inf,inf], "",
      "Solvent scattering length density" ],
    ]

# No volume normalization despite having a volume parameter
# This should perhaps be volume normalized?
form_volume = """
    return 1.0;
    """

Iq = """
    const double qsq = q*q;
        const double drh = head_sld - solvent_sld;
        const double drt = sld  - solvent_sld;          //correction 13FEB06 by L.Porcar
        const double qT = q*tail_length;
        double Pq, inten;
        Pq = drh*(sin(q*(head_length+tail_length))-sin(qT)) + drt*sin(qT);
        Pq *= Pq;
        Pq *= 4.0/(qsq);
        
        inten = 2.0e-4*M_PI*Pq/qsq;     
        
        return inten /= 2.0*(head_length+tail_length);  //normalize by the bilayer thickness    
                
    """
        
Iqxy = """
    // never called since no orientation or magnetic parameters.
    return -1.0;
    """

# ER defaults to 0.0
# VR defaults to 1.0

demo = dict(
        scale=1, background=0,
                tail_length=15,head_length=10,
        sld=0.4, head_sld=3.0, solvent_sld=6.0,
                tail_length_pd= 0.2, tail_length_pd_n=40,
                head_length_pd= 0.01, head_length_pd_n=40,
          )
oldname = 'LamellarFFHGModel'
oldpars = dict(head_length='h_thickness', sld='sld_tail', head_sld='sld_head', solvent_sld='sld_solvent')